LOCAL CLIMATOLOGY. 69 



institute a proportion in which these results may be compared with 

 those obtained by actual experiment with such a standard. Starting 

 mth the commonly received 80° Fahrenheit as the average for the 

 equator, although Humboldt gives it as 81°. 5, we have all the elements 

 of such a calculation at our command, and the proportion is : 



As .958, the sine of the average altitude of the sun at the equator, multiplied by 

 12, the length of the day at the equator, and this product multiplied by .6, the 

 average of the sines of the altitude for the day (being the correction for 

 the absorption of heat by the atmosphere) ; 



is to 80° Fahrenheit (the average for the year at the equator) : 



so is the sine of the sun's altitude at noon for any day or latitude multiplied into the 

 length of the day, and this product multiplied by the average altitude of 

 the sun for the day ; 



to the temperature for the day in degrees of Fahrenheit. 



Or, to put the formula into a briefer form : 



Let sin. A stand for the sine of the altitude at noon, D for the length of the day, and 

 C for the correction of the average of the altitude at the equator; then sin. A' and D' 

 and C' will stand for corresponding values for any day in any other latitude ; and we have, 

 with T for temperature : 



As sin. A X D X C : 80° : : sin. A' X D' X C' : T. 



If now we call D, in the first term of the first ratio, unity, and make 

 D' a fraction obtained by dividing the length of the day between sunrise 

 and sunset by 12, we shall simplify the operation of computing for the 

 values of T. 



By the use of this formula, I have computed the average temperature, 

 with that for the hottest and for the coldest season, for each latitude in 

 the northern hemisphere.* 



* The results given in this Table differ somewhat from those that have been previously given, 

 especially in giving a lower temperature for the higher latitudes ; and as the importance that 

 should be attached to the results of any computation depend alike on its method and on its data, 

 I give, for the satisfaction of those who may desire it, the brief outline of both. 



Let S and S' denote the sun at different altitudes, S being perpen- 

 dicular. Then S' will denote the sun at a declination from the zenith 

 equal to the angle SaS', which angle we will call the zenith distance 

 of the sun, or simply Z. Now it is manifest that a ray of heat com- 

 ing from the sun at S, and dispersed over one square foot, ab, will 

 become dispersed over a rectangle elongated to ac, when the sun has 

 declined to S' ; and this elongation is equal to the secant of Z. Hence 



the intensity of the light in the rectangle ac will be ; that on 



sec.Z 



the square aft being unity. But = cos., and the cosine of any 



sec. 



angle is equal to the sine of the complement ; but the complement of Z is the sun's altitude, or 



angular distance from the horizon. 



Hence there can be no doubt that the sine of the sun's altitude = sin. A, is an expression for 



the intensity of the sun's rays at any place or time, after deducting what is absorbed, or perhaps 



